Observational evidence, including offshore moraines and sediment cores, confirm that at the Last Glacial Maximum (LGM) the Greenland ice sheet (GrIS) expanded to a significantly larger spatial extent than seen at present, grounding into Baffin Bay and out onto the continental shelf break. Given this larger spatial extent and its close proximity to the neighbouring Laurentide Ice Sheet (LIS) and Innuitian Ice Sheet (IIS), it is likely these ice sheets will have had a strong non-local influence on the spatial and temporal behaviour of the GrIS. Most previous paleo ice-sheet modelling simulations recreated an ice sheet that either did not extend out onto the continental shelf or utilized a simplified marine ice parameterization which did not fully include the effect of ice shelves or neglected the sensitivity of the GrIS to this non-local bedrock signal from the surrounding ice sheets. In this paper, we investigated the evolution of the GrIS over the two most recent glacial-interglacial cycles (240 ka BP to the present day) using the ice-sheet-ice-shelf model IMAU-ICE. We investigated the solid earth influence of the LIS and IIS via an offline relative sea level (RSL) forcing generated by a glacial isostatic adjustment (GIA) model. The RSL forcing governed the spatial and temporal pattern of sub-ice-shelf melting via changes in the water depth below the ice shelves. In the ensemble of simulations, at the glacial maximums, the GrIS coalesced with the IIS to the north and expanded to the continental shelf break to the southwest but remained too restricted to the northeast. In terms of the global mean sea level contribution, at the Last Interglacial (LIG) and LGM the ice sheet added 1.46 and -2.59 m, respectively. This LGM contribution by the GrIS is considerably higher (∼1.26 m) than most previous studies whereas the contribution to the LIG highstand is lower (∼0.7 m). The spatial and temporal behaviour of the northern margin was highly variable in all simulations, controlled by the sub-ice-shelf melting which was dictated by the RSL forcing and the glacial history of the IIS and LIS. In contrast, the southwestern part of the ice sheet was insensitive to these forcings, with a uniform response in all simulations controlled by the surface air temperature, derived from ice cores.